Abstract
In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant C± background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with C± fluxes. We generalize this result to other embeddings. We find new distinctive rotating membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume. We obtain numerical and analytical solutions in different approximations characterizing the dynamics of the membrane with fluxes C± for different ansätze of the dynamical degrees of freedom. Finally we discuss the physical admissibility of some of these ansätze to model the components of the symplectic gauge field.
Highlights
Of Q-ball matrix model [5], as instantonic solutions [6], or in terms of membranes formulated on hyperkähler backgrounds [7, 8]
We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations
In this work we obtain some solutions to the equations of motion (E.O.M) associated to the bosonic sector of the supermembrane toroidally compactified on M9×T 2 formulated on the Light Cone Gauge (LCG) on a C± background
Summary
We analyze the system of equations that represents the dynamics of the supermembrane on a quantized constant background field C±. In order to reproduce the BRR energy expression MBRR from the M2-brane with fluxes theory in the LCG, we fix the background component of the three-form C+ = 0 imposing a non-vanishing flux condition over C− and we assume Ar to be constant with Za and Xr satisfying the embedding ansatz given by (4.1). We have shown that the BRR results can be obtained from the M2-brane with fluxes once the background is fixed, i.e. C+ = 0 and we have frozen the dynamical degree of freedom associated to the gauge symplectic connection Ar and the ansatz (4.1) is assumed This background has restricted the APD constraint expression to the one used by [20]. BRR spinning solutions that satisfy the C− flux condition (2.13) are naturally contained in the allowed spinning solutions of the M2-brane with C± fluxes
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